We have carried out continuum observations of the Sgr B2 molecular cloud at 1300 μm using the 14 m Five College Radio Astronomy Observatory (FCRAO) telescope, and at 1100, 850, 450, and 350 μm using the James Clerk Maxwell telescope (JCMT). These data, obtained with ≃20″ resolution, offer the first detailed description of the submillimeter radiation from this complex source. The emission is dominated by the middle and northern compact sources, but we have detected for the first time the far-infrared radiation associated with the Northeast H II region L of Benson and Johnston, as well as from the southern H II region/molecular maser source H. Our data, together with existing infrared measurements, indicate that the optical depth within Sgr B2(N) is significantly greater than that of Sgr B2(M) and that it has a noticeable effect for λ ≤ 800 μm. The envelope of Sgr B2(M) becomes optically thick for the radiation from Sgr B2(N), located within it, for wavelengths ≤ 100 μm. From radiative transfer modeling, we obtain a luminosity of 107 L⊙ for the middle source and 2 × 106 L⊙ for the northern source.